Defining N-ary Relations on the Semantic Web: Use With Individuals

W3C Working Draft 21 July 2004

This version:

https://www.w3.org/TR/2004/WD-swbp-n-aryRelations-20040721

Latest version:

https://www.w3.org/TR/swbp-n-aryRelations

Previous versions

This is the first public Working Draft

Editors:

Natasha Noy, Stanford University

Alan Rector, University of Manchester

Copyright ©2004 W3C^® (MIT, ERCIM, Keio), All Rights Reserved. W3C liability, trademark and document use rules apply.

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Abstract

In Semantic Web languages, such as RDF and OWL, a property is a binary relation; that is, it links two individuals or an individual and a value. How do we represent relations among more than two individuals? How do we represent properties of a relation, such as our certainty about it, severity or strength of a relation, relevance of a relation, and so on? The document presents ontology patterns for representing n-ary relations and discusses what users must consider when choosing these patterns.

Status of this Document

This section describes the status of this document at the time of its publication. Other documents may supersede this document. A list of current W3C publications and the latest revision of this technical report can be found in the W3C technical reports index at https://www.w3.org/TR/.

This document is intended to be a part of a future W3C Working Group Note that will provide an introduction and overview of all ontology design patterns produced by the Semantic Web Best Practices and Deployment Working Group, part of the W3C Semantic Web Activity.

This document is a W3C Working Draft and is expected to change. The SWBPD WG does not expect this document to become a Recommendation. Rather, after further development, review and refinement, it will be published and maintained as a WG Note.

This document is the First Public Working Draft. We encourage public comments. Please send comments to public-swbp-wg@w3.org [archive] and start the subject line of the message with "comment:"

• The addition of an argument-list pattern [1]
• The addition of an Appendix showing a Topics Map solution [2]
• Use of skolemization instead of blank nodes [3]
• Different namespaces for A-Box and T-Box [3]

Publication as a Working Draft does not imply endorsement by the W3C Membership. This is a draft document and may be updated, replaced or obsoleted by other documents at any time. It is inappropriate to cite this document as other than work in progress.

General issue

In Semantic Web languages, such as RDF and OWL, a property is a binary relation: it links two individuals or an individual and a value. How do we represent relations among more than two individuals? How do we represent properties of a relation, such as our certainty about it, severity or strength of a relation, relevance of a relation, and so on?

Use case examples

Several common use cases fall under the category of n-ary relations. Here are some examples:

1. Christine has breast tumor with high probability. There is a binary relation between the person Christine and diagnosis breast_tumor and there is a qualitative probability value describing this relation (high).
2. Steve has temperature, which is high, but falling. The individual Steve has two values for two different aspects of a has_temperature relation: its magnitude is high and its trend is falling.
3. John buys a "Lenny the Lion" book from books.example.com for $15 as a birthday gift. There is a relation, in which individual John, entity books.example.com and the book Lenny_the_Lion participate. This relation has other values such as the purpose (birthday_gift) and the amount ($15).

Representation pattern

In Semantic Web languages, such as RDF and OWL, we have only binary relations (properties) between individuals, such as a property P between an individual A and individual B (more precisely, P is the property of A with the value B):

We would like to have another individual or simple value C to be part of this relation:

In other words, P is now a relation among A, B, and C.

A common solution to representing n-ary relations such as these is to create an individual which stands for an instance of the relation and relates the things that are involved in that instance of the relation. We can think of the original relation then as a class of all these relation instances.

Depending on the relation between A, B, and C, we distinguish two patterns to represent n-ary relations in RDF and OWL:

In the first case (pattern 1), one of the individuals in the relation (say, A) is distinguished from others in that it is the originator of the relation. Just like in the case of binary relation, where P was a property of A with value B, here the instance of the relation itself is a property of A, with the value that is a complex object in itself, relating several values and individuals. Examples 1 and 2 from the list above fall under this category: Christine and Steve in these examples are individuals that the properties are describing.

In the second case (pattern 2), the n-ary relation represents a network of participants that all play different roles in the relation, but two or more of the participants have equal "importance" in the relation. Example 3 above would usually fall into this category: At least John, books.example.com, and the Lenny_The_Lion book seem to be equally important in this purchasing relation.

An interested reader may also want to look at the discussion of reification [3] and rdf:value [4] in RDF.

Pattern 1:

If we need to represent a value describing a relation (example 1, Christine has breast tumor with high probability) or represent an object of a relation that has different aspects (example 2, Steve has temperature, which is high, but falling), we can create an individual that includes the relation object itself, as well as the additional information about the object:

For the example 1 above (Christine has breast tumor with high probability), the individual Christine has a property has_diagnosis that has another object (Diagnosis_Relation_1, an instance of the relation Diagnosis_Relation) as its value:

The individual Diagnosis_Relation_1 here represents a single object both the diagnosis (breast_tumor) and the probability of the diagnosis (HIGH)¹:

:Christine
      a       :Person ;
      :has_diagnosis :Diagnosis_Relation_1 .

:Diagnosis_Relation_1
      a       :Diagnosis_Relation ;
      :diagnosis_probability :HIGH;
      :diagnosis_value :Breast_Tumor .

The corresponding class definitions look as follows:

The additional labels on the links indicate the OWL restrictions on the properties. We define both diagnosis_value and diagnosis_probability as functional properties. We also require that each individual Diagnosis_Relation has exactly one value for Disease.

In RDFS, the links represent rdfs:range constraints on the properties. For example, the class Diagnosis_Relation is the range of the property has_diagnosis.

Here is a definition of the class Diagnosis_Relation in OWL, assuming that both properties--diagnosis_value and diagnosis_probability--are defined as functional (we provide full code for the example in OWL and RDFS below):

:Diagnosis_Relation
      a       owl:Class ;
      rdfs:subClassOf
              [ a       owl:Restriction ;
                owl:someValuesFrom :Disease ;
                owl:onProperty :diagnosis_value
              ] ;
      rdfs:subClassOf
              [ a       owl:Restriction ;
                owl:allValuesFrom :Probability_values ;
                owl:onProperty :diagnosis_probability
              ] .

In the definition of the Person class (of which the individual Christine is an instance) we specify a property has_diagnosis with the range restriction going to the Diagnosis_Relation class (of which Diagnosis_Relation_1 is an instance):

:Person
      a       owl:Class ;
      rdfs:subClassOf
              [ a       owl:Restriction ;
                owl:allValuesFrom :Diagnosis_Relation ;
                owl:onProperty :has_diagnosis
              ] .

RDFS code for this example

[RDFS]

OWL code for this example

We have a different use case in the example 2 above (Steve has temperature, which is high, but falling): In the example with the diagnosis, many will view the relationship we were representing as in a fact still a binary relation between the individual Christine and the diagnosis breast_tumor that has a probability associated with it. The relation in this example is between the individual Steve and the object representing different aspects of the temperature he has. In most intended interpretations, this relation cannot be viewed as a binary relation with additional attributes attached to it. Rather it is a relation between the individual Steve and the complex object representing different facts about his temperature.

The RDFS and OWL patterns that implement this intuition are however the same as in the previous example. A class Person (of which the individual Steve is an instance) has a property has_temperature which has as a range the relation class Temperature_Relation. Instances of the class Temperature_Relation (such as Temperature_Relation_1 in the figure) in turn have properties for temperature_value and temperature_trend.

RDFS code for this example

[RDFS]

OWL code for this example

[N3] [RDF/XML] [Abstract syntax]

Pattern 2:

In some cases, the n-ary relationship represents a network of individuals that play different roles in a structure without any single individual standing out as the originator or the owner of the relation, such as Purchase in the example 3 above (John buys a "Lenny the Lion" book from books.example.com for $15 as a birthday gift). Here, the relation explicitly has more than one participant, and, in many contexts, none of them can be considered a primary one. In this case, we create an individual to represent the relation with links to all participants:

In our specific example, the representation will look as follows:

Purchase_1 is an individual instance of the Purchase class representing a relation:²

:Purchase_1
      a       :Purchase ;
      :buyer :John ;
      :object :Lenny_The_Lion ;
      :purpose :Birthday_Gift ;
      :seller :books.example.com .

The following diagram shows the corresponding classes and properties. For the sake of the example, we specify that each purchase has exactly one buyer (a Person), exactly one seller (a Company) and at least one object (an Object).

The diagram refers to OWL restrictions. In RDFS the arrows can be treated as rdfs:range links.

The class Purchase is defined as follows in OWL (see the RDFS file below for the definition in RDFS):

:Purchase
      a       owl:Class ;
      rdfs:subClassOf
              [ a       owl:Restriction ;
                owl:allValuesFrom :Purpose ;
                owl:onProperty :purpose
              ] ;
      rdfs:subClassOf
              [ a       owl:Restriction ;
                owl:cardinality 1 ;
                owl:onProperty :buyer
              ] ;
      rdfs:subClassOf
              [ a       owl:Restriction ;
                owl:onProperty :buyer ;
                owl:someValuesFrom :Person
              ] ;
      rdfs:subClassOf
              [ a       owl:Restriction ;
                owl:cardinality 1 ;
                owl:onProperty :seller
              ] ;
      rdfs:subClassOf
              [ a       owl:Restriction ;
                owl:onProperty :seller ;
                owl:someValuesFrom :Company
              ] ;
      rdfs:subClassOf
              [ a       owl:Restriction ;
                owl:onProperty :object ;
                owl:someValuesFrom :Object
              ] .

RDFS code for this example

[RDFS]

OWL code for this example

Considerations when representing n-ary relations

• In many cases, the choice between the two patterns above is subjective. We have described the difference in terms of the relative importance of various participants in the relation. In many cases, making this judgment will be difficult, and both pattern will be appropriate. For instance, if we want to represent the fact that, in human anatomy, head and neck are adjacent along the vertical axis, we can look at this relation in two ways.
  (1) We want to specify a is_adjacent_to property for the head, and the value of that property is a relation linking it to the neck and specifying the axis as an additional attribute in the relation (pattern 1)
  (2) We want to specify an individual adjacency_relation that has head and neck as its two values for the property object and vertical as the value for the property axis.
• In our example, we did not give meaningful names to the individuals representing relations (We do give meaningful names to the corresponding classes though). These individuals usually play auxiliary purpose of grouping together several objects and do not stand on their own. As a result, it is common not to have meaningful names for them (in particular if following pattern 1) and refer to them only in the context of individuals and properties for which they are the values. Note that a similar approach is taken when reifying statements in RDF.
• OWL allows definition of inverse properties. Defining inverse properties with n-ary relations, using any of the two patterns above, requires more work than with binary relations. Each of the properties participating in the n-ary relation should have its own inverse property (with the proper constraints). Consider the example of John buying the Lenny_The_Lion book. We may want to have an inverse relation pointing from the Lenny_The_Lion book to the person who bought it. If we had a simple binary relation John buys Lenny_The_Lion, defining an inverse is simple: we simply define a property is_bought_by as an inverse of buys:
  

  :is_bought_by
        a       owl:ObjectProperty ;
        owl:inverseOf :buys .

  With the purchase relation represented as an instance, however, we need to add inverse relations between participants in the relation and the instance relation itself:
  
  For example, the definitions of the inverse relations for for agent and object of a purchase, look as follows:
  

  :is_buyer_for
        a       owl:ObjectProperty ;
        owl:inverseOf :buyer .
  :is_object_for
        a       owl:ObjectProperty ;
        owl:inverseOf :has_object .

  And the definition of the Person class (taking into account the inverse for the recipient property) is:
  

  :Person
        a       owl:Class ;
        rdfs:subClassOf
                [ a       owl:Restriction ;
                  owl:onProperty :is_buyer_for ;
                  owl:allValuesFrom :Purchase
                ] .

  Note that the value of the inverse property is_buyer_for for the individual John, for example, is the individual Purchase_1 rather than the object or recipient of the purchase.

Notes

1. For simplicity, we represent each disease as an individual. This decision may not always be appropriate, and we refer the reader to a different note (ref to be added). Similarly, for simplicity, in OWL we represent probability values as a class that is an enumeration of three individuals (HIGH, MEDIUM, and LOW):

   :Probability_values
         a       owl:Class ;
         owl:equivalentClass
                 [ a       owl:Class ;
                   owl:oneOf (:HIGH :MEDIUM :LOW)
                 ] . 

   There are other ways to represent partitions of values. Please refer to a different note (ref to be added). In RDF Schema version, we represent them simply as strings, also for simplicity reasons.

2. For simplicity, we will ignore the fact that the amount is expressed in $ and will use a simply number as the value for the property. For a discussion on how to represent units and quantities in OWL, please refer to a different note (ref to be added)

References

[1] https://lists.w3.org/Archives/Public/public-swbp-wg/2004May/0091.html

[2] https://lists.w3.org/Archives/Public/public-swbp-wg/2004May/0016.html

[3] https://lists.w3.org/Archives/Public/public-swbp-wg/2004Jul/0009.html

[4] https://www.w3.org/TR/2004/REC-rdf-primer-20040210/#reification

[5] https://www.w3.org/TR/2004/REC-rdf-primer-20040210/#rdfvalue